We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.
finite element method, obstacle problem, a posteriori error estimate, functional majorant, variational inequalities, Uzawa algorithm
34B15, 65K15, 65L60, 74K05, 74M15, 74S05